\section{Closed Loop Analysis}

\frame{
  \frametitle{Outline}
  \tableofcontents[sectionstyle=show/shaded,subsectionstyle=hide]
}

\subsection{Closed Loop Analysis}

\frame[t]{
\frametitle{Poles and Zeros of the Closed Loop Plant Model}
   \only<1>{
    \vspace{3mm}
    \begin{itemize}
      \item
        No unstable poles.
      \item
        Minimum phase system.
    \end{itemize}
    \begin{figure}
      \centering
      \vspace{-1mm}
      \includegraphics[height=0.45\textheight]{poleszeros_lsys_cl}
      \caption{Real parts of the poles and zeros as a function of hip displacement.}
    \end{figure}
  }
}

\frame[t]{
\frametitle{Sensitivity Singular Values of the Closed loop Plant Model}
   \only<1>{
    \vspace{3mm}
    \begin{itemize}
      \item
        Small maximum singular values indicate good nominal performance.
    \end{itemize}
    \begin{figure}
      \centering
      \vspace{-1mm}
      \includegraphics[height=0.4\textheight]{singularvalues_STFM_cl}
      \caption{Maximum singular value of the sensitivity transfer function matrix as a function of hip displacement.}
    \end{figure}
  }
}

\frame[t]{
\frametitle{Singular Values of the Closed Loop Plant Model}
   \only<1>{
    \vspace{-3mm}
    \begin{figure}
      \centering
      \vspace{-1mm}
      \includegraphics[width=0.75\textwidth]{singularvalues_pchip_cl}
      \caption{Singular values as a function of hip displacement.}
    \end{figure}
  }
}

\frame[t]{
\frametitle{Singular Values of the Closed Loop Plant Model}
   \only<1>{
    \vspace{3mm}
    \begin{itemize}
      \item
        Good stability robustness at low frequencies.
      \item
        Robust stability becomes unreliable at high frequencies
    \end{itemize}
    \begin{figure}
      \centering
      \vspace{-1mm}
      \includegraphics[height=0.4\textheight]{singularvalues_cl}
      \caption{Singular values as a function of hip displacement.}
    \end{figure}
 }
}
